Vector Algebra PYQs - Last 10 Years

AP EAPCET / Mathematics / Algebra / 123 recent questions

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Practice 123 AP EAPCET Mathematics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Vector Algebra Questions

Showing 23 of 123 filtered questions.

1Vector Algebra

If \(P\) and \(Q\) are two points on the curve \(y=2^{x+2}\) in the rectangular cartesian coordinate system such that \(\mathbf{O P} \cdot \hat{i}=-1, \mathrm{OQ} \cdot \hat{i}=2\), then \(\mathrm{OQ}-4 \mathrm{OP}=\)

2Vector Algebra

Let \(\mathbf{a}=\hat{\mathbf{i}}\) and \(\mathbf{b}=\hat{\mathbf{j}}\), the point of intersection of the lines \(\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a}\) and \(\mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}\) ...

3Vector Algebra

If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

4Vector Algebra

Let \(\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}\) and \(\mathbf{w}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). Then which of the following statement is t...

5Vector Algebra

The position vectors of the points \(A\) and \(B\) with respect to \(O\) are \(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). The length of the internal bisector of...

6Vector Algebra

Given, \(\mathbf{a}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=\mathbf{b}_1+\mathbf{b}_2\) where \(\mathbf{b}_1\) is parallel to \(\mathbf{a}\) and $$\mathbf{b}_...

7Vector Algebra

Let \(u\) and \(v\) be two non-zero vectors in \(R^3\) with the intermediate angle \(45^{\circ}\). Then \(|\mathbf{u} \times \mathbf{v}|\) is equal to

8Vector Algebra

Let \(\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}\) if \(\mathbf{d}\) is a unit vector such $$\mathbf{a} \cdot \mathbf{b}=0=[\mathbf{b} \mat...

9Vector Algebra

The value of \(\frac{(\mathbf{a} \times \mathbf{b})^2+(\mathbf{a} \cdot \mathbf{b})^2}{2(\mathbf{a})^2(\mathbf{b})^2}\) is

10Vector Algebra

The point of intersection of the lines joining points \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(-\hat{\mathbf{i}}, 2 \hat{\mathbf{i}}\) is

11Vector Algebra

Let \(u=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(v=3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}\). Consider three points \(P, Q\) and \(R\) having the position vectors $$\left(\frac{5}{2}\right) \hat{\mathbf{i}}-2 \hat{\mathbf{j}} ;\left(\frac{...

12Vector Algebra

If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=x \hat{\mathbf{i}}+(x-2) \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and if the vector $$\mathbf{...

13Vector Algebra

If \(\mathbf{a}\) and \(\mathbf{b}\) are two vectors such that \(|\mathbf{a}|=2, |\mathbf{b}|=3\) and \(\mathbf{a}+t \mathbf{b}\) and \(\mathbf{a}-t \mathbf{b}\) are perpendicular, where \(t\) is a positive scalar, then

14Vector Algebra

Let \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(\mathbf{c}=7 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}\), then the area of parallel...

15Vector Algebra

If \(\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}\) and \(\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}}{2}\), then angle between \(\mathbf{a}+\mathbf{b}\) and \(\mathbf{a}-\mathbf{b}\) is

16Vector Algebra

If the volume of the parallelopiped formed by the vectors \(\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+a \hat{\mathbf{k}}\) and \(a \hat{\mathbf{i}}+\hat{\mathbf{k}}\) becomes minimum, then \(a\) is equal to

17Vector Algebra

Angle made by the position vector of the point (5, \(-\)4, \(-\)3) with the positive direction of X-axis is

18Vector Algebra

A vector makes equal angles \(\alpha\) with \(X\) and \(Y\)-axis, and \(90 \Upsilon\) with \(Z\)-axis. Then, \(\alpha\) is equal to
(c) 45Yand 135Y
(d) $90 \mathrm{Y}$

19Vector Algebra

Let \(x\) and \(y\) are real numbers. If \(\mathbf{a}=(\sin x) \hat{\mathbf{i}}+(\sin y) \hat{\mathbf{j}}\) and \(\mathbf{b}=(\cos x) \hat{\mathbf{i}}+(\cos y) \hat{\mathbf{j}}\), then \(|\mathbf{a} \times \mathbf{b}|\) is

20Vector Algebra

Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be three-unit vectors and \(\mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cdot \mathbf{c}=0\). If the angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\). Then $$[\mathbf{a b c}]^...

21Vector Algebra

If \(\mathbf{a}\) and \(\mathbf{b}\) are two vectors such that \(\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|} < 0\) and \(|\mathbf{a} \cdot \mathbf{b}|=|\mathbf{a} \times \mathbf{b}|\) then the angle between the vectors $$\m...

22Vector Algebra

If \(\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), and \(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) are position vectors of \(A, B\) and \(C\) respectively an...

23Vector Algebra

Which of the following vector is equally inclined with the coordinate axes?